PHYSICAL REVIEW B 83, 104419 (2011)

Effect of Si doping and applied pressure upon magnetostructural properties of Tb5 (Si x Ge1−x )4 magnetocaloric compounds Yuan-Chieh Tseng,1,* Hao-Jhong Ma,1 Chao-Yao Yang,1 Yaroslav Mudryk,2 Vitalij K. Pecharsky,2,3 Karl A. Gschneidner Jr.,2,3 Narcizo M. Souza-Neto,4 and Daniel Haskel4 1

Department of Materials Science and Engineering, National Chiao Tung University, Hsin-chu 30010, Taiwan 2 Division of Materials Science and Engineering, The Ames Laboratory, Ames, Iowa 50011-3020, USA. 3 Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011-2300, USA. 4 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 9 December 2010; revised manuscript received 20 January 2011; published 28 March 2011)

The composition- and pressure-dependent magnetostructural properties of Tb5 (Six Ge1−x )4 (x = 0.4, 0.485, 0.625, and 0.7) were investigated using x-ray powder diffraction and x-ray magnetic circular dichroism in a diamond anvil cell, respectively. Substituting the smaller-size Si for Ge stabilizes a single-phase, ferromagnetic (FM) orthorhombic O(I) structure for x  0.7. Similarly, application of external pressure causes a canted antiferromagnetic orthorhombic O(II) sample (x = 0.4) to transform into an FM O(I) phase at 4 GPa. The elementand orbital-specific x-ray absorption data indicate that the Tb 4f orbital occupation changes with external pressure, likely through 4f-5d electronic mixing, yet no changes in Tb 4f electronic structure are observed with Si doping. The results point to different mechanisms behind the enhancement of FM exchange interactions in Tb5 (Six Ge1 x )4 with chemical and applied pressure, respectively. DOI: 10.1103/PhysRevB.83.104419

PACS number(s): 75.30.Sg

I. INTRODUCTION

In recent years, magnetic refrigeration technology has been considered an alternative to traditional vapor-compression refrigeration because of its environmentally friendly nature.1–3 Materials exhibiting a strong magnetocaloric effect4 (MCE) are at the heart of magnetic cooling technology. Among numerous magnetocaloric material candidates, the R5 (Six Ge1−x )4 family (R = rare earth) has drawn much attention due to the strong coupling between structural and magnetic properties that leads to a giant MCE.3,5–8 The best-known members of the family, Gd5 (Six Ge1−x )4 compounds,2,3 show a linearly increasing Curie temperature (TC ) with Si doping up to near room temperature, greatly enhancing the potential of magnetic cooling for room temperature applications. Replacing Gd with Tb modifies the magnetic properties significantly9–11 partly due to the different single-ion anisotropies (Gd is isotropic while the 4f electron wave functions of Tb lack spherical symmetry) and modifications in the electronic band structure. Key differences between Gd5 (Six Ge1−x )4 and Tb5 (Six Ge1−x )4 include the persistence of antiferromagnetism (AFM) to much higher Si concentrations in the Tb case and the decoupling of magnetic and structural transitions for 0.35 < x < 0.65 in the Tb family9 versus the coupled magnetostructural transition for x  0.5 in the Gd family.2,3 The magnetostructural properties of Tb5 (Six Ge1−x )4 are less studied relative to its Gd5 (Six Ge1−x )4 counterpart. Our previous studies have focused on the Si-Ge sites of Gd5 (Six Ge1−x )4 , understanding the correlation between bondbreaking and magnetic ordering during the first-order, coupled magnetostructural transitions,3,12 as well as the correspondence between Si doping (chemical pressure) and applied pressure in enhancing the magnetic ordering temperature, using x-ray magnetic circular dichroism (XMCD) at low temperature and high pressures.13–15 This work is aimed at understanding the influence of the rare-earth site on the magnetostructural 1098-0121/2011/83(10)/104419(7)

phase diagram, probing the nature of the uncoupled magnetic and structural transitions for Tb5 (Six Ge1−x )4 and their evolution with Si doping and pressure. We present results from x-ray diffraction experiments showing that the four chosen samples (x = 0.4, 0.485, 0.625, and 0.7) are characterized by different structural ground states. These, in turn, are intimately connected to the compounds’ magnetic properties and their response to applied pressure, as probed by XMCD measurements. The complexity of the Tb5 (Six Ge1−x )4 system contrasts with that of Gd5 (Six Ge1−x )4 , where a ferromagnetic orthorhombic (I) [FM O(I)] ground state is observed for x  0.125. This work facilitates the understanding of the interplay between magnetism, electronic structure, and crystal structure in the Tb5 (Six Ge1−x )4 system . II. EXPERIMENT

Polycrystalline powder samples of Tb5 (Six Ge1−x )4 with x = 0.4, 0.485, 0.625, and 0.7 were prepared as described by Zou et al.16 These four compositions were chosen because they cover the region of the Tb5 (Six Ge1−x )4 phase diagram where magnetic and structural transitions decouple by 5–10 K.9 This allows a direct comparison with Gd5 (Six Ge1−x )4 which displays a fully coupled magnetostructural transition for x  0.5. The samples were ground into fine powders for x-ray measurements. Low-temperature (10 K) powder x-ray diffraction (XRD) measurements were performed at the BL01C2 beamline of the National Synchrotron Radiation Research Center (NSRRC), Taiwan, with a wavelength of ˚ (25 keV). Two-dimensional diffraction patterns 0.495941 A were collected by a Mar345 image plate, and the collected diffraction rings were integrated with the FIT2D program17 into a diffraction pattern of intensity versus scattering angle 2θ . Rietveld refinement18 was used to determine the crystallographic structures and the lattice constants. The low-temperature crystal structures of x = 0.485 and 0.625

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samples were verified independently using data obtained from a standard rotating-anode powder diffractometer equipped with a low-temperature attachment and Mo Kα radiation.19 The magnetization studies [isothermal and isofield fieldcooled (FC), and zero-field-cooled (ZFC) measurements] were conducted using a superconducting quantum interference device (SQUID) magnetometer. The high-pressure (HP) x-ray magnetic circular dichroism setup13 located at beamline 4ID-D of the Advanced Photon Source at Argonne National Laboratory was employed to probe the pressure-induced magnetic transitions of the samples. The gap between the pole pieces of an electromagnet needed to accommodate the diamond anvil cell13 resulted in a magnetic field (H) of ∼0.45 T. The XMCD signals were collected over the Tb L3 edge (2p → 5d electric dipole transition at 7.514 keV) in helicity-switching mode, and data accuracy was verified by consecutive measurements under reverse applied field. X-ray absorption near-edge structure (XANES) spectra were simultaneously acquired to monitor changes in the electronic structure with Si doping and applied pressure. III. RESULTS

The XRD patterns measured at 10 K and ambient pressure condition for the four samples, together with Rietveld refinements using the models of monoclinic (M), orthorhombic (I) [O(I)], orthorhombic (II) [O(II)], and mixed-phase [M + O(I)], are presented in Fig. 1. The results reveal the ground-state crystal structures of the samples. The Tb5 (Si0.4 Ge0.6 )4 compound is characterized by a single-phase, O(II) structure. Both Tb5 (Si0.485 Ge0.515 )4 and Tb5 (Si0.625 Ge0.375 )4 are mixed-phase M + O(I) compounds, with Tb5 (Si0.625 Ge0.375 )4 having a larger volume fraction of the O(I) phase than Tb5 (Si0.485 Ge0.515 )4 . The Tb5 (Si0.7 Ge0.3 )4 compound presents a single-phase, O(I) structure. The concentrations of the M phase were ∼53% (65%) and ∼15% (25%) for Tb5 (Si0.485 Ge0.515 )4 and Tb5 (Si0.625 Ge0.375 )4 , respectively, based on the data recorded using rotating-anode (synchrotron) radiation. The variation in absolute phase fractions for each composition may be attributed to different preferred orientations of physically different specimens used in the two types of measurements. Figure 2 shows the M-H curves for the four samples at T = 10 K, the same temperature at which the XRD patterns were collected. The inset shows the saturation magnetization (Ms ) and remnant magnetization (Mr ) as a function of Si content and O(I) concentration. The Tb5 (Si0.4 Ge0.6 )4 sample exhibits a hysteresis loop that is far from square, and magnetization that only approaches saturation at ∼4 T. The significant hysteresis accompanying the change in field direction, as indicated by the arrows, suggests a possible partially irreversible field-induced AFM → FM phase transition, similar to the observation in Gd5 Ge4 .20,21 Alternatively, the presence of competing AFM and FM interactions in zero field could be responsible for the reduced (but finite) Mr and observed differences in FC and ZFC data [Fig. 3(a)]. For the other three samples, the concentration of the ferromagnetic component (as derived from the squareness of the hysteresis loop, remanence, and low-field saturation) increases with Si doping; all samples show much reduced hysteresis compared to Tb5 (Si0.4 Ge0.6 )4 .

FIG. 1. (Color online) X-ray diffraction patterns of (a) Tb5 (Si0.4 Ge0.6 )4 , (b) Tb5 (Si0.485 Ge0.515 )4 , (c) Tb5 (Si0.625 Ge0.375 )4 , and (d) Tb5 (Si0.7 Ge0.3 )4 at T = 10 K, together with results of Rietveld refinements using models of single-phase O(II) (a), mixed-phase M + O(I) (b) and (c), and single-phase O(I) (d) crystal structures. Gray lines at the bottom of the plot represent the difference between the experimental and theoretical intensities.

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FIG. 2. (Color online) Isothermal M-H data for Tb5 (Si0.4 Ge0.6 )4 , Tb5 (Si0.485 Ge0.515 )4 , Tb5 (Si0.625 Ge0.375 )4 , and Tb5 (Si0.7 Ge0.3 )4 , collected at T = 10 K. Arrows indicate the directions of the change of magnetic field in Tb5 (Si0.4 Ge0.6 )4 . The inset shows Ms (filled squares, left-hand axis) and Mr (open squares, right-hand axis) as a function of Si content. The O(I) concentrations for the four samples are marked on top of the open squares.

The samples reach a saturation magnetization of ∼200 emu/g at 5 T, the value reported by Zou et al.22 in a single-crystal Tb5 (Si0.55 Ge0.45 )4 sample with the magnetic field applied along the a axis (the easy magnetization direction). Since the saturation magnetization is markedly different for field applied along the b and c directions, our data indicate that the powder samples were oriented in the field (easy axis along the field direction). The slightly reduced saturation for x = 0.4 is likely due to an incomplete field-induced AFM[O(II)] → FM[O(I)] transition in this sample. These trends in M-H curves for Tb5 (Si0.485 Ge0.515 )4 , Tb5 (Si0.625 Ge0.375 )4 , and Tb5 (Si0.7 Ge0.3 )4 correlate well with the increasing fraction of the O(I) phase detected from XRD, which is generally linked to a FM phase in the R5 (Six Ge1−x )4 family (see inset in Fig. 2). In addition, these data are consistent with previous reports11,16 showing that the saturation magnetization of the monoclinic phase is smaller than that of the O(I) phase. Temperature-dependent FC and ZFC measurements on warming are summarized in Fig. 3, showing the magnetic properties of the four samples and their evolution with Si doping. An increase in transition temperature from 70 to 210 K is observed with increasing Si content, consistent with the magnetostructural phase diagram.7 Nevertheless, a notable irreversibility between FC and ZFC data is observed in Tb5 (Si0.4 Ge0.6 )4 , Tb5 (Si0.485 Ge0.515 )4 , and Tb5 (Si0.625 Ge0.375 )4 samples; the irreversibility diminishes with increasing Si concentration and finally nearly disappears in Tb5 (Si0.7 Ge0.3 )4 . Temperature-dependent integrated XMCD intensities for Tb5 (Si0.4 Ge0.6 )4 at various pressures are shown in Fig. 4(a). The nonzero XMCD at ambient pressure and low temperature is due to either the canting of an AFM structure under the H = 0.45 T applied field or the presence of reduced ferromagnetism due to competing AFM and FM interactions in the x = 0.4 sample. Irreversibility in FC and ZFC SQUID

FIG. 3. Temperature-dependent magnetization data of (a) Tb5 (Si0.4 Ge0.6 )4 , (b) Tb5 (Si0.485 Ge0.515 )4 , (c) Tb5 (Si0.625 Ge0.375 )4 , and (d) Tb5 (Si0.7 Ge0.3 )4 measured on warming at H = 0.45 T, after field cooling (open circles) and zero-field cooling (filled circles).

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FIG. 4. Temperature-dependent integrated XMCD data of (a) Tb5 (Si0.4 Ge0.6 )4 taken at various pressures and (b) Tb5 (Si0.4 Ge0.6 )4 , Tb5 (Si0.485 Ge0.515 )4 , Tb5 (Si0.625 Ge0.375 )4 , and Tb5 (Si0.7 Ge0.3 )4 taken at ambient pressure. Both data sets were measured on warming. The lines are guides to the eye.

data (Fig. 3), together with finite remnant magnetization (Fig. 2), indicate that the latter scenario is more likely. The enhanced XMCD signals at higher pressures are due to a pressure-induced stabilization of the FM state. The details will be discussed below. Figure 4(b) shows temperature-dependent, integrated XMCD intensities at ambient condition for the four samples. Figures 4(a) and 4(b) depict the correspondence between pressure and Si doping in affecting the magnetic properties. Figure 5 presents the (a) Si- and (b) pressure-dependent Tb L3 -edge XMCD data collected at T = 10(2) K (normalized to the x-ray absorption jump). XANES spectra for both are also displayed to show where the XMCD quadrupolar (2p → 4f) and dipolar signals are located relative to the edge. The insets confirm the reversal of the XMCD signal upon field switching. The data reveal the details for the electronic modifications upon Si doping and increasing pressure. As expected, the magnetization is enhanced by both Si doping and applied pressure, which is consistent with what has been found in the low-x, mixed-phase regime (x  0.125) of Gd5 (Six Ge1−x )4 .13 For the pressure-dependent result, the XMCD signal does not increase any further in the 4 – 7 GPa range, indicating that a fully saturated FM state has been reached. Although

FIG. 5. (a) Doping- and (b) pressure-dependent (x = 0.4) Tb L3 edge XANES (upper curves) and XMCD (lower curves) data. Arrows indicate the numeral scales for XANES (right axis) and XMCD (left axis). The XMCD data are normalized to the absorption jump. Data were collected at H = 0.45 T and T = 10(2) K. The insets show the reversal of XMCD signal upon reversal of the applied field. For clarity, XANES data in (b) are only shown at ambient pressure and 1.5 and 7.0 GPa.

the XMCD signal at base temperature reaches saturation, the magnetic ordering temperature keeps increasing from 4 to 7 GPa as shown in Fig. 4(a). For the L3 -edge XMCD of rare-earth compounds, it is expected that the quadrupolar (2p → 4f ) and dipolar (2p → 5d) contributions dominate the onset and higher excitation energies of the spectrum, respectively.23–25 For the pressureinduced transition [Fig. 5(b)], the XMCD quadrupolar contribution becomes more prominent with the increase of pressure, whereas it is barely noticeable with Si doping [Fig. 5(a)]. The enhancement of the quadrupolar channel occurs along with an asymmetric broadening of the XMCD line shape and a decrease in XANES white line peak intensity. Although the decrease in XANES peak intensity could be due to band broadening alone, the concomitant increase in the 4f contribution is likely indicative of a change in orbital occupation. The different responses of the XMCD quadrupolar contribution to doping and pressure can be clearly seen in the inset panels of Figs. 5(a) and 5(b), which correspond to the

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FIG. 6. (Color online) Pressure dependencies of Tt for Gd5 (Si0.375 Ge0.625 )4 (open circles, taken from Ref. 23) and Tb5 (Si0.4 Ge0.6 )4 (filled circles). Dashed line shown for Tb5 (Si0.4 Ge0.6 )4 corresponds to a dTt /dP of ∼1.35 K kbar 1 for P > 4 GPa, which is close to 1.5 K kbar−1 observed in Gd5 (Si0.375 Ge0.625 )4 . Solid line for Tb5 (Si0.4 Ge0.6 )4 is the extrapolation of the low-pressure linear behavior.

largest chemical (x = 0.7) and physical pressure (P = 7 GPa), respectively. Figure 6 compares the pressure dependence of magnetic transition temperature, dTt /dP , for Gd5 (Si0.375 Ge0.625 )4 and Tb5 (Si0.4 Ge0.6 )4 , where the data for Gd5 (Si0.375 Ge0.625 )4 are taken from our previous work.26 The pressure dependence of Tt for Tb5 (Si0.4 Ge0.6 )4 is obtained from Fig. 4(a), in which Tt is defined as the maximum in the absolute value of the data’s first derivative. Generally, this Tt corresponds to a 60% reduction in XMCD signal relative to its saturated value at low T. These two particular compounds were chosen because of their close Si content, allowing us to compare dTt /dP in the different structural ground states of the two families [Gd5 (Si0.375 Ge0.625 )4 is O(I), but Tb5 (Si0.4 Ge0.6 )4 is O(II) at ambient pressure]. As can be seen in the figure, Tb5 (Si0.4 Ge0.6 )4 exhibits a larger dTt /dP (1.9 K kbar−1 ) than Gd5 (Si0.375 Ge0.625 )4 (1.5 K kbar−1 ) up to 4 GPa. However, the two become comparable after P = 4 GPa. IV. DISCUSSION

As follows from the M(H) and M(T) data shown in Figs. 2 and 3, the O(II) structure of Tb5 (Si0.4 Ge0.6 )4 results in a canted AFM O(II) (weakly ferromagnetic) magnetostructural ground state in zero field. This is expected since at this Si doping level ferromagnetic interactions only begin to compete with predominantly AFM interactions. This is in fair agreement with the magnetostructural phase diagram of Tb5 (Six Ge1−x )4 reported by Ritter et al.,7 in which the AFM O(II) ground state is present up to x ∼ 0.35. The presence of magnetocrystalline anisotropy,9,10 together with the polycrystalline nature of the sample, results in nonzero FM signal in magnetization data. The R5 (Six Ge1−x )4 compounds are quite sensitive to applied field, temperature, and pressure, all of which affect the interslab bonding. As a consequence, the significant hysteresis

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seen in the M(H) data of Tb5 (Si0.4 Ge0.6 )4 is likely due to a field-induced canted AFM → FM transition, similar to what is observed in Gd5 Ge4 .20,21 The transition is complete at μ0 H = 4 T, and the magnetization as a function of the reduced field refers to the remaining FM fraction as a result of hysteresis. The influence of the applied field on the canted AFM O(II) phase of Tb5 (Si0.4 Ge0.6 )5 may also be responsible for a significant irreversibility between ZFC and FC data on warming. A mixed [M + O(I)] ferromagnetic state for Tb5 (Si0.5 Ge0.5 )4 has been reported by Morellon et al.,11,27 where both M and O(I) structures are found to support long-range FM ordering. However, the ferromagnetic [M + O(I)] ground state reported here for Tb5 (Si0.485 Ge0.515 )4 and Tb5 (Si0.625 Ge0.375 )4 samples (determined by XRD and SQUID data) is not fully consistent with the previous findings.11,27 In our study, the monoclinic phase is observed even at temperatures as low as 10 K, while Morellon et al.11 report 100% O(I) phase already at T = 85 K for Tb5 Si2 Ge2 . Such discrepancy may originate from the fact that our samples have slightly different Si : Ge ratios when compared to Tb5 Si2 Ge2 , especially considering that properties of alloys in the Tb5 (Six Ge1−x )4 system are quite sensitive to the variation of composition (x). However, we believe that the main difference in the phase content at low temperatures originates from the difference in the chemical purity of the rare-earth metals used in the preparation of the alloys. In our study we have used the most pure Tb prepared by Materials Preparation Center (MPC) of Ames Laboratory, which has significantly lower amounts of interstitial impurities (oxygen, nitrogen, and carbon) compared to the commercially available metals used in Ref. 9. In a closely related Gd5 Six Ge4−x system, the lower purity of the starting Gd metal promotes the formation of the O(I) phase. For example, Hardy et al.28 report a significant concentration (∼30%) of FM component in the zero-field-cooled M(H) data for the Gd5 Ge4 compound, which is not found in the high-purity Gd5 Ge4 sample.29 Since the O(II) Gd5 Ge4 structure does not support ferromagnetism, it is a clear indication that the impurities promote formation of the O(I) FM structure in the Gd5 (Six Ge1−x )4 system. Another characteristic example of the purity effect on the magnetostructural behavior in R5 T4 (T is (Six Ge1−x )) systems is the Er5 Si4 compound. The structural O(I) to M transition was observed upon cooling in this system in the samples that were prepared using high-purity erbium,30,31 but the sample prepared using the commercially available Er contains the O(I) phase only at all measured temperatures.32 Therefore, it is reasonable to assume that using lower-purity Tb (as in Ref. 9) promotes the stability of the O(I) phase in the Tb5 Six Ge4−x series of alloys, while our samples prepared using high-purity Tb may and do indeed contain measurable amounts of the monoclinic phase. In general, the O(I) structure describes a slab-connected, fully ordered FM state. Thus, the FM-M state can be thought of as a suppressed FM state due to the magnetic frustration arising from the partially disconnected slabs of the M structure. The magnetic moment of the Tb atoms located closer to the broken T-T bonds in monoclinic Tb5 Si2 Ge2 are much smaller than the rest of the Tb moments.27 Such magnetic frustration weakens ferromagnetism upon cooling as evidenced by the

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ZFC-FC irreversibility (Fig. 3) and the lower saturation magnetization (inset of Fig. 2). The presence of the FM-M phase indicates a decoupled magnetostructural transition,27 leading to a reduced MCE in Tb5 (Six Ge1−x )4 compared to Gd5 (Six Ge1−x )4 . Adding Si eliminates the FM-M phase from the ground state, as confirmed by a fully restored FM O(I) phase in Tb5 (Si0.7 Ge0.3 )4 . For this composition, the ZFCFC irreversibility nearly disappears and a higher ordering temperature is observed due to strengthened FM exchange interactions. Our previous work shows that the magnetostructural properties of R5 (Six Ge1−x )4 can be modified by Si doping and/or applied pressure in a similar fashion. For Gd5 (Six Ge1−x )4 , both Si doping and applied pressure trigger an AFM O(II) → FM O(I) transition involving the reforming of interslab bonding, along with a linear enhancement of TC .12,13 For Tb5 (Six Ge1−x )4 , XRD (Fig. 1) and SQUID (Fig. 3) results show that Si doping causes a canted AFM O(II) to FM O(I) transformation. It is, therefore, reasonable to expect that pressure would result in the same transition, based on the analogy with the Gd-based compounds. This is indeed seen in Fig. 4. For Tb5 (Si0.4 Ge0.6 )4 , the canted AFM O(II) → FM O(I) transition can also be realized by pressure, which confirms the existence of the Si doping– pressure correspondence in Tb5 (Six Ge1−x )4 . This finding is in agreement with previous pressure-dependent results reported for Tb5 (Si0.5 Ge0.5 )4 ,27 and extends the Si doping–pressure correspondence to higher pressures. Note that once the canted AFM O(II) to FM O(I) transition is complete, further increases in pressure stabilize FM ordering by increasing the transition temperature alone, as can be seen in the data at 4 and 7 GPa [Fig. 4(a)]. Although the canted AFM → FM transition can be achieved by either Si doping or pressure, they occur with different electronic modifications. This is highlighted in Fig. 5, where the XANES white line peak intensity decreases with increasing pressure, but not with Si doping. Furthermore, the line shapes of Tb L3 -edge XMCD are similar for low and high Si doping, but they are markedly different for ambient- and high-pressure data at the position where the quadrupolar contribution dominates. For Tb5 (Six Ge1−x )4 , pressure causes a detectable increase in the XMCD quadrupolar feature, perhaps due to a lifting of 4f states across the Fermi level accompanied by changes in 5d occupation. It is important to note that the XMCD of Tb5 (Si0.4 Ge0.6 )4 at P = 7 GPa is expected to be close to that of Tb5 (Si0.7 Ge0.3 )4 at ambient pressure, because both of them reach a fully saturated FM O(I) ground state. However, the dipolar XMCD signal at P = 7 GPa is smaller than that of Tb5 (Si0.7 Ge0.3 )4 by ∼12%. Considering the concomitant increase in quadrupolar XMCD signal the result suggests that there is likely a 4f-5d charge transfer taking place while the material undergoes the transition under pressure (but to a much lesser extent upon Si doping). The enhanced XMCD signal in the quadrupolar channel indicates that such newly formed empty 4f states are spin polarized. The decrease of the XANES intensity in the dipolar channel with pressure could be due to a related decrease in the empty Tb 5d states in the vicinity of the Fermi level, also responsible for the broadening of the XMCD signal. Such putative 4f-5d hybridization could facilitate FM interactions

and lead to increasing magnetic ordering temperatures. Since the transition temperature keeps increasing from 4 to 7 GPa even though the 4f-5d hybridization does not, the strength of indirect FM exchange in Tb5 (Six Ge1−x )4 is not only regulated by this assumed 4f-5d hybridization. Additional contributions to the enhancement of the ordering temperature for P > 4 GPa may come from increased 5d–Si (Ge) p hybridization, as was observed in Gd5 (Six Ge1−x )4 .12 Density functional theoretical calculations in the local density + U approximation (LDA + U) are needed in order to address the exact nature of the pressure-induced changes in electronic structure. On the other hand, the 4f-5d orbital hybridization is minor in Gd5 (Six Ge1−x )4 where XMCD broadening and enhancement of quadrupolar features, either in a pressure-induced AFM → FM transition33 or in the further stabilization of the FM state with pressure,14 are much less visible relative to Tb5 (Six Ge1−x )4 . The enhanced stability of the half-filled 4f 7 configuration of Gd relative to the 4f 8 configuration of Tb may explain why changes in 4f electron occupation and hybridization are observed in the Tb (but not in the Gd) case, even at these moderately low pressures. Furthermore, the sizable single-ion anisotropy of Tb relative to the negligible anisotropy of Gd affects how structural modifications under pressure couple to the 4f electronic structure and magnetic ordering.22 In the case of Gd5 (Six Ge1−x )4 the pressure-induced increase in the FM exchange interactions, as well as the increase in the transition temperature, are mainly facilitated by the change in Gd 5d–Si (Ge) p hybridization just as with Si doping, rather than by the 4f-5d hybridization seen in Tb5 (Six Ge1−x )4 . This indicates that, although a Si concentration–pressure correspondence is seen in both Tb5 (Six Ge1−x )4 and Gd5 (Six Ge1−x )4 , the mechanism by which the strength of FM exchange is regulated differs between the two. The results suggest that in terms of the electronic structure, the Si concentration–pressure correspondence in Tb5 (Six Ge1−x )4 is even more complex than that in Gd5 (Six Ge1−x )4 . The nature of the magnetostructural ground state, in addition to the electronic structure, also determines the response of Tb5 (Six Ge1−x )4 to pressure. As shown in Fig. 6, Tb5 (Si0.4 Ge0.6 )4 yields a discontinuous dTt /dP as a result of the change in the ground state. The large dTt /dP for P < 4 GPa is due to an effective pressure-induced, first-order canted AFM O(II) → FM O(I) transition involving the reforming of the interslab bonds, leading to a sudden stabilization of the FM state. However, for P > 4 GPa where the FM O(I) state is fully restored in Tb5 (Si0.4 Ge0.6 )4 , the compound exhibits a smaller dTc /dP , comparable to that of Gd5 (Si0.375 Ge0.625 )4 , whose ground state is known to be FM O(I). In the latter case, pressure acts to stabilize the FM O(I) state, slowly increasing Tt . V. CONCLUSION

We have measured, using SQUID, XRD, and XMCD probes, the magnetostructural properties of Tb5 (Six Ge1−x )4 (x = 0.4, 0.485, 0.625, and 0.7) in response to Si doping and applied pressure. It is found that a full FM O(I) ground state is only observed for x  0.7, while the other three samples display either canted AFM O(II) (x = 0.4) or mixed FM [M + O(I)]

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(x = 0.485 and 0.625) phases. The Tb5 (Six Ge1−x )4 family responds to Si doping and pressure in a similar way, resulting in the FM O(I) ground state when the canted AFM O(II) phase of x = 0.4 is doped with Si or subjected to pressure. This is similar to its Gd counterpart.14,15 However, a remarkable electronic modification involving Tb 4f and 5d states accompanies the canted AFM → FM transition in Tb5 (Six Ge1−x )4 with pressure but not with Si doping. Such involvement of 4f states does not appear to occur in Gd5 (Six Ge1−x )4 . The larger sensitivity of 4f states to pressure in the Tb system lies in its modified electronic band structure relative to that of the Gd system. In addition, the dTt /dP is strongly dependent on the material’s magnetostructural ground state, another factor that determines the Tb5 (Six Ge1−x )4 response to pressure.

*

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PHYSICAL REVIEW B 83, 104419 (2011) ACKNOWLEDGMENTS

The authors would like to thank Hwo-Shuenn Hsu and Wei-Tsung Chuang for their help in XRD data collection at the BL01C2 beamline of the National Synchrotron Radiation Research Center at Taiwan. Work at National Chiao Tung University is supported by the National Science Council of Taiwan under Grant No. NSC 98-2112-M-009 022-MY3. Work at Argonne is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC-02-06CH11357. Work at Ames Laboratory is supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering under Contract No. DE-AC02-07CH11358 with Iowa State University.

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